Mueller reportedly planned to ask Trump about a dinner and meetings he had with Comey, for example - the details of which make up a thread of the obstruction-of-justice case against Trump.
Mueller also wants to know about the two publicly known occasions in which Trump moved to fire the special counsel, the questions show, according to The Times.
Mueller's list of questions for Trump was obtained and reported on by The New York Times on Monday.
Comey's firing by Trump last May paved the way for Deputy Attorney General Rod Rosenstein to hire Mueller to investigate the meddling allegations and possible collusion between Trump's campaign and Russian Federation.
Numerous questions obtained by The Times focus on the obstruction issue, including Mr Trump's angry criticism of Attorney-General Jeff Sessions' recusal from the Russian Federation investigation.
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Speaking to CNN, John Dean, the White House counsel for President Richard Nixon, suggested the questions as reported in The Times sounded more like "these are questions somebody wrote down after listening to someone else" rather than necessarily being "designed by the prosecutors".
The questions also touch on the Russian meddling and whether the Trump campaign coordinated with the Kremlin in any way. He is believed to be cooperating with Mueller. Mueller specifically asks what communication Trump had with Russian government officials and the Agalrovs, an Azerbaijani-Russian family who partnered with Trump on the pageant.
Mueller also wants to quiz Trump about whether he knew about Russian hacking during the campaign. He was sacked on February 13, 2017 - purportedly because he lied to Vice President Mike Pence about the phone calls.
What did you know about phone calls that Mr. Flynn made with the Russian ambassador, Sergey I. Kislyak, in late December 2016?
Since at least early this year, Mueller has discussed the possibility of interviewing Trump for the investigation, according to the president's attorneys. Another question on the list states. His lawyers have been negotiating terms of an interview out of concern that their client - whose exaggerations, half-truths and outright falsehoods are well documented - could provide false statements or easily become distracted.